Relation Definition and 1000 Threads

Homework Statement The position of a 60-gram golf ball sitting on a tee is determined within +- 1μm. What is its minimum possi- ble energy? Moving at the speed corresponding to this kinetic energy, how far would the ball move in a year?Homework Equations ## K\geq\dfrac {\hbar ^{2}} {2ma^{2}}...

If Neanderthals and humans interbred, then they must have had a common ancestor that was also human. What is known about this common ancestor?

When can be used (\frac{\partial S}{\partial V})=\frac{P}{T}?

Hello, Something I have some time wondering and still couldn't find the answer is to this question: if there is some relation between the Spectrum (functional analysis) and the Frequency spectrum in Fourier Analysis. Now that I think about it there seems to be a casuality the use of the...

Is it the absence and presence of an electrical fluid called as positive and negative charges?

Why is dU=-\vec{F}.d\vec{r} Integrating with putting the limits on we get: ΔU=-W Why is this? Here \vec{F} is a conservative force/Force field.

I'm having a gap in understanding the relation between them, and resolving my confusion is really appreciated. For example, the Hamiltonian operator, why do we call its eigenvalues energies? how do we actually measure it in the laboratory, quantum mechanically? And maybe I need a better...

Hello all. This is not a "What is Energy" Thread but rather a question about its relation with work. I understand that energy has been defined as the ability to do work. So why is change in energy is equal to work? Cant energy be equal to work. Also when the force field is doing work on...

I am read the pag 190 of Dodelson bock, where use the following relation \rho_{DM}= \rho \frac{y}{y+1} . where y= a/a_{eq}=\rho_{DM}/\rho_{rad} i tried using the tipically relation \rho = \rho_{rad} a^-4+ \rho_{DM} but, i don't understand, healp please

So I understand that Reynolds number is the ratio of intertial forces to viscous forces but how exactly does this relate to flow? Why is it that when viscous forces dominate one gets a laminar flow? How to conceptualize?

Homework Statement Prove that the relation, two finite sets are equivalent if there is a one-to-one correspondence between them, is an equivalence relation on the collection S of all finite sets. I'm sure I know the gist of how to do it, but I'm a beginner in proofs, and I'm not sure if...

I found this in Srednicki's QFTbook. I don't know what ↔ means. Help me, please

One can show that at around ##p \approx m## where m is the physical mass the full propagator ##D_F## is something like $$D_F = \frac{Z}{p^2 - m^2}.$$ Where ##Z = (1 - \Sigma '(m))^{-1}##, ##\Sigma## is the self energy and m is the physical mass of the particle. If i were now to write a...

Hi,I hope my question will be clear.I need to be explained me one problem.That is: Can be expressed physical law,for example average speed like relation,but not like a function?Or speed can be only the function?I mean,why we use functions to describe physical phenomena?Is possible to describe...

I've just started learning about torque, and understand that tau=Fd, but wondered how this relates to F=ma. For example if there is a rod with a pivot in the middle (say a nail), when one end is pushed down, why does the other end move up? Where is the force that causes the end to move up...

Please explain the relation between electric potential energy and electric field in detail.

Stability, Helmholtz free energy mathematical relation "proof" Homework Statement I must show that \left ( \frac{\partial ^2 F}{\partial V ^2} \right ) _T=\frac{\frac{\partial ^2 U}{\partial S^2} \frac{\partial ^2 U}{\partial V ^2} - \left ( \frac{\partial ^2 U}{\partial S \partial V} \right...

We know that electrons are nearly massless so their wave funtion is quite easily detectable.So is there any mathematical relation between the mass of the body and the intensity of the wave it exhibits? thanks

Homework Statement Prove the commutation relation ##\left [L_x, p_y \right] = i\hbar \epsilon_{xyz} p_z## Homework Equations ##L_x = yp_z - zp_y## ##p_z = i\hbar \frac{\partial}{\partial z}##The Attempt at a Solution ##\left [L_x, p_y \right] = (yp_z - zp_y)p_y - p_y(yp_z - zp_y)## ##\left...

Homework Statement Have a solution for the temperature u(x,t) of a heated rod, now using the orthogonality relation below show that the coefficients a_n , n = 0,1,2,... can be expressed as: a_n = \frac{2}{L} \int_{0}^{L} cos\frac{n\pi x}{L} f(x) dx Homework Equations \int_{0}^{L}...

Relation between Cooling rate and Viscosity Hi all I have a situation where i have a molten Aluminium Copper alloy melt poured in a mould to be solidified. This means, the mould temperature is lower than than than the poured melt. I am thinking about a relation which associates temperature...

I see there have been many postings about this topic in this forum. The formula for this relation is Luminosity = Mass^3.5 Taking logs of both sides we get log (lum) = 3.5 * log (mass) and using a little algebra we find that the exponent (3.5) should equal log (lum) ÷ log (mass) I have...

Hi. is there anyone who is familiar with surface wave plasma discharges? I want to solve dispersion equation of surface waves in cylindrical plasma column,numerically,to obtain "phase diagram" and "attenuation diagram" from dispersion equation solving. But this dispersion equation include...

I'm confused about the condition for spontaneity for the Helmholtz energy. My textbook (McQuarrie, "Physical Chemistry") derives the conditions as follows. We start with the combined law of thermodynamics: dU = δq + δw ≤ TdS – PdV since δq/T ≤ dS dU – TdS + PdV ≤ 0 For a process at...

Homework Statement Let A be the set that contains all rational numbers, but not zero. Let (a,b),(c,d) \in A×A. Let (a,b)\tilde{}(c,d) if and only if ad = bc. Prove that \tilde{} is an equivalence relation on A×A.Homework Equations The Attempt at a Solution The solution just needs to show...

Hello!Could you help me at the exercie below? Consider a gamble,with the same possibility to win or to lose.If we win,we double our property,but if we lose we halve our property.Let's consider that we begin with an amount c.Which will be the mean value of our property,if we play n...

Hi all, What is the relation between RAMAN Intensity and Energy of the photon and/or bond stregth and/or bond energy? Is there any equation or sth explain it easily? If you can explain it in a simple way, I will appreciate. Thanks

Hello friends, If we consider ##{T}## as coordinate time and ##{\tau}## as proper time, the relationship between them is: ##\frac{T}{\tau}= \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}## so, ##{T}= \frac{\tau}{\sqrt{1-\frac{v^2}{c^2}}}## So we can consider this expression like this: If In...

I am familiar with the equation ΔG=ΔG°+RT ln(Q).But I can't derive it.We have to use the equation to derive nernst equation. So please help.

Homework Statement The **mean value theorem** says that there exists a $c∈(u,v)$ such that $$f(v)-f(u)=f′(c)(v-u).$$ Here is my question. Assume that $u$ is a root of $f$, hence we obtain $$f(v)=f′(c)(v-u);$$ assume that $f$ is a non-zero analytic function in the whole real line. We...

Hi Guys, I am learning some solid state physics. I see a lot of pictures with Phonon Dispersion Relation, with \omega (\vec{k}) on the y-axis and \Gamma, X, M, \Gamma, R on the x-axis. I don't understand, why the angular frequenzy \omega (\vec{k}) is important. Or why is this...

Homework Statement Homework Equations The Attempt at a Solution Is my initial assumption wrong?

Homework Statement a_{n} = a_{n-1} + n a_{0} = 0 The Attempt at a Solution h_{n} = h_{n-1} t^{2} - t = 0 t=0 t=1 h_{n} = B p_{n} = bn + c p_{n} = p_{n-1} + n bn + c = b(n-1) + n bn + c = (b+1)n -b I'm sure I've gone wrong somewhere, I just can't figure out where!

Hi I'm doing Fourier analysis in my signals and system course and I'm looking at the solution to one basic problem but I'm having trouble understanding one step Can anyone explain to me why becomes From Eulers formula: http://i.imgur.com/1LtTiKX.png for example the Cosine in my problem. I...

Ultra cold atom is achieved by laser cooling. For optical lattice, it is achieved by the interference of counter-propagating laser beams. What is the relation between Ultra-cold atom and optical lattice? Why do people load Ultra-cold atom in optical lattice? Thank you for your answer.

Hello Want to know if constant speed of light is a result cause by time dilation? When your time slow down as you approach speed of light you take a longer time to measure light speed in your spaceship, there for you think speed of light relative to your current speed is still c? When one...

So I am given B=\begin{array}{cc} 3 & 5 \\ 5 & 3 \end{array}. I find the eigenvalues and eigenvectors: 8, -2, and (1, 1), (1, -1), respectively. I am then told to form the matrix of normalised eigenvectors, S, and I do, then to find S^{-1}BS, which, with S = \frac{1}{\sqrt{2}}\begin{array}{cc} 1...

Homework Statement I am wondering what is the relation of sinθ & time of flight in projectile motion with angle. (under the case of same velocity) Is the graph of this in a parabola shape?? Homework Equations t = (2u sinθ) / g (u in constant) The Attempt at a Solution would it be...

Given a discrete time signal x[n] that has a DTFT (which exists in the mean square convergence or in the uniform convergence sense), how can we tell if the signal x[n] converges absolutely? I know the following: x[n] is absolutely summable <=> X(e^{j \omega}) converges uniformly (i.e...

This is a question out of model theory. (This preamble is due to the fact that "model" and "theory" are used in different ways in different fields.) Is there any specific relationship between two theories which have the same models? A knee-jerk reaction would be to say that they are isomorphic...

Homework Statement Find a recurrence relation for the number of stricly increasing sequences of positive integers that have 1 as their first term and n as their last term, where n is a positive integer. that is, sequences a1, a2, ..., ak, where a1 = 1, ak = n, and aj < aj+1 for j = 1, 2...

Homework Statement Hi guys, I'm stuck at some step in a QM exercise. Here it is: Consider a free particle of mass m that moves along the x-axis (1 dimensional). Show that ##\frac{dA}{dt}=\frac{2 \hbar ^2}{m^2}\int \frac{\partial \psi}{\partial x} \frac{\partial \psi ^*}{\partial...

I am trying to figure out the torque vs weight relationship. I am working on a software project where I want to create an application to determine the maximum payload on vehicle with rubber tyre on asphalt road. I am having three parameter 1. Torque 2. RPM 3. Diameter of tyre based on...

What is the relation between the pressure that is exerted on the internal walls of a cylinder and the characteristics of a flow of water running inside it? Let's assume that the flow velocity is constant and that we have an inviscid flow of pipe flow type. Furthermore let's assume that the...

Hello all, Is the following equality true \int(f(x))^*\,dx=\left(\int(f(x))\,dx\right)^*. Thanks

In GR for orbits about a central mass in the Schwarzschild metric one can show that \dot r^2 = \frac{E^2}{m^2 c^2} - (1-\frac{r_s}{r})(c^2 + \frac{p_\phi^2}{r^2}). where E=-p_t, r_s is the Schwarzschild radius and 'dot' represent differentiation with respect to proper time. Similarly for...

The integral form of Ampere's law in vacuum is ∫B\cdotdl=μ_{0}I (a) Using the relation between I and J, obtain the differential form of Ampere's law. You may ignore any displacement current. (b)Define the displacement current density J_{d} in terms of the displacement field D and show...

Homework Statement I have seen case studies of the 3D Debye model where the vibrational modes of a solid is taken to be harmonic with dispersion relation \omega = c_sk. It is said that for temperatures much less than the Debye temperature, the heat capacity at constant volume C_V\sim T^3...

Regarding the relation between atoms' kinetic energy and the energy levels of their electrons upon excitation: In other words, what really happens when an atom is excited, either by radiation or by collisions, or otherwise ? What are the mechanisms under which the transferred energy goes to...

When making the transition from the dispersion relation for a beaded string to the relation for a continuous string, I'm confused about the following issue. Take a to be the spacing between beads, m the mass of each bead, and T the tension in the string. We assume these to be constant. For the...